Lwaxana is many things, but vulgar is not one of them.
Well, that's a matter of opinion, & even in this case, culture. If she is indeed publicly falsifying lustfulness in Picard's thoughts, which Deanna potentially confirms when she says it's a joke, & she also publicly flaunts her man servants' pornographic thoughts about her, if she invites someone to a meal under false pretenses to make advances (Which we do love to drag Geordi about) & declares that the crew of the ship will be her pool of potential conquests, if she publicly shames her own daughter for not having done similar... you know, to some people, perhaps not people from Betazed, but some people... that could be considered vulgar.
It's not as if anyone is calling her obscene, but I mean all "vulgar" amounts to is being rude, unrefined, course, or obvious, & frankly, what is it about her that people on that ship found taxing about having her around? It's those attributes. They actually tolerate it to greater extents from her, because she's both a dignitary, & related to a respected member of the crew. Plus, her behavior might be more common within her culture. I really doubt if Riker's dad had come aboard displaying the same behavior we'd be as readily accepting of it.
For example, Picard once called Ardra vulgar, for chasing/pursuing him, & making similarly overt advances. Now Lwaxana is not an unscrupulous con artist, but that bit of behavior itself seems similarly crude... at least potentially to him.
Admittedly, I agree with
@Feltman_Langer that as they spent time depicting her more well-roundedly, especially on DS9, those aspects seemed to fall away more & more, but it's not necessarily incorrect to suggest Picard might have found her, at one time, vulgar, especially if being obvious is not "tantalizing" to him.
Consider now Vash, who is also somewhat brash & untamed, but not so much intimately overt or obvious. When he thought she was, after planting that kiss on him... not interested in her at all, but when the reality came out of what she was truly like, brother did that change.